It wasn't day to night, there was a dusk shot in there before the chase goes into the tunnel, and also a time jump when we see Dagget watching the chase on the news at night.

I noticed that the last time I watched the movie. There's a shot of Foley outside the stock exchange after the chase with Bane starts that is at dusk. And a good portion of the chase is in the tunnels, allowing time progression. It isn't a continuity error as I originally thought.